Experimental Realization of Classical $\mathbb{Z}_2$ Spin Liquids in a Programmable Quantum Device

TL;DR

This paper demonstrates the experimental realization of classical $$ spin liquids using a programmable quantum device, revealing phase transitions and loop structures, and discusses potential pathways to quantum spin liquids for topological qubits.

Contribution

We experimentally realize and probe classical $$ spin liquids on a quantum device, showing control over phase transitions and vertex weights, and outline future steps towards quantum spin liquids.

Findings

Observation of classical 8-vertex and 6-vertex states and transitions.

Control over vertex weights and phase diagram.

Device configurations consistent with theoretical models.

Abstract

We build and probe a $\mathbb{Z}_2$ spin liquid in a programmable quantum device, the D-Wave DW-2000Q. Specifically, we observe the classical 8-vertex and 6-vertex (spin ice) states and transitions between them. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry using only pairwise-qubit interactions and a transverse field, i.e., interactions which are accessible in this quantum device. The combinatorial gauge symmetry remains exact along the full quantum annealing path, landing the system onto the classical 8-vertex model at the endpoint of the path. The output configurations from the device allows us to directly observe the loop structure of the classical model. Moreover, we deform the Hamiltonian so as to vary the weights of the 8 vertices and show that we can selectively attain the classical 6-vertex (ice) model, or drive the system into a ferromagnetic state. We present studies of the classical phase diagram of the system as function of the 8-vertex deformations and effective temperature, which we control by varying the relative strengths of the programmable couplings, and we show that the experimental results are consistent with theoretical analysis. Finally, we identify additional capabilities that, if added to these devices, would allow us to realize $\mathbb{Z}_2$ quantum spin liquids on which to build topological qubits.